For printing - MSP

Now if n1 ≥ 2, l ∈ S1, then
(4.38)
I q
β,i2···in Π j∈S1\{l}[A j
ij
HÖLDER REGULARITY FOR ∂ 253
(z)] 1
i j
·
R2n1 +1
[A l 1
i
il (z)] l
·
2 q |r(z)| + |ζ1| +
2 q |r(z)| +
m
k∈S1\{l} t=2
Now apply Lemma 3.7 to (4.38) with
(4.39)
to get
(4.40)
+ A l il
il |ζl|
a = 2 q |r(z)| + |ζ1| +
a ′ = 2 q |r(z)| +
k∈S1,k=l
k = il, α = 2 +
I q
β,i2···in Π j∈S1\{l}[A j
ij
·
R2n1−1 ⎛
⎛
(z)] 1
i j
ij
j∈S1,j=l
⎝2 q |r(z)| +
k∈S1\{l} t=2
k∈S1\{l}
A k t (z)|ζk| t
|ζk| + |ζ1| + |ζl|
−2− P
j∈S 1 ,j=l 1
i j − 1
i l −κ
m
|ζk| + |ζ1|
1
k∈S1\{l}
· ⎝2 q |r(z)| + |ζ1| +
k∈S1\{l} t=2
A k t (z)|ζk| t
+ κ, α ′ = n1 − 2 + κ > 0
⎞
|ζk| + |ζ1| ⎠
m
A k t (z)|ζk| t
−n1+2−κ
⎞
⎠
−n1+1−κ
dV (ζ).
−2− P
j∈S1 ,j=l 1
−κ ij dV (ζ).